10 citations · 27 across the 8 of their papers we have counts for
14 papers
Asymptotics for the Laplace transform of the time integral of the geometric Brownian motion
Dan Pirjol, Lingjiong Zhu
We present an asymptotic result for the Laplace transform of the time integral of the geometric Brownian motion with $X_T = \int_0^T e^{σW_s + ( a…
Fractal Structure and Generalization Properties of Stochastic Optimization Algorithms
Alexander Camuto, George Deligiannidis, Murat A. Erdogdu +3
Understanding generalization in deep learning has been one of the major challenges in statistical learning theory over the last decade. While recent work has illustrated that the d…
Convergence Rates of Stochastic Gradient Descent under Infinite Noise Variance
Hongjian Wang, Mert Gürbüzbalaban, Lingjiong Zhu +2
Recent studies have provided both empirical and theoretical evidence illustrating that heavy tails can emerge in stochastic gradient descent (SGD) in various scenarios. Such heavy…
Asymmetric Heavy Tails and Implicit Bias in Gaussian Noise Injections
Alexander Camuto, Xiaoyu Wang, Lingjiong Zhu +3
Gaussian noise injections (GNIs) are a family of simple and widely-used regularisation methods for training neural networks, where one injects additive or multiplicative Gaussian n…
Non-Convex Optimization via Non-Reversible Stochastic Gradient Langevin Dynamics
Yuanhan Hu, Xiaoyu Wang, Xuefeng Gao +2
Stochastic Gradient Langevin Dynamics (SGLD) is a powerful algorithm for optimizing a non-convex objective, where a controlled and properly scaled Gaussian noise is added to the st…
Fractional Underdamped Langevin Dynamics: Retargeting SGD with Momentum under Heavy-Tailed Gradient Noise
Umut Şimşekli, Lingjiong Zhu, Yee Whye Teh +1
Stochastic gradient descent with momentum (SGDm) is one of the most popular optimization algorithms in deep learning. While there is a rich theory of SGDm for convex problems, the…